Robotic avatar technology has the potential to impact the future of human connectivity, transporting the sense of a human’s presence to a remote location anywhere and in real-time. In this regard, the recent ANA Avatar XPRIZE challenge fostered the development of the ultimate generation of non-autonomous robotic avatar designs. This paper is devoted to introducing our system proposal, allowing intuitive motion-based control and multi-modal feedback. The teleoperated robot endorses an anthropomorphic upper body with dual arms and dexterous hands for fine manipulation of even small objects, as well as an omnidirectional platform for improved and safe locomotion. Special focus is pointed at the crucial challenge of providing self-body perception to the operator, in particular regarding control of the arms and rendering of haptic sensations. To this end, we propose an upper-limb exoskeleton and a teleoperation architecture allowing retargeting of the operator’s skills and receiving tactile and kinesthetic force feedback with realistic and informative perception of the own’s arms. Lastly, the platform was validated during laboratory and challenge missions mimicking several social, cooperative, and cultural scenarios from which we report on the lesson learned and future improvements.